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On the lengths of pairs of complex matrices of size at most five

Published online by Cambridge University Press:  17 April 2009

W. E. Longstaff ,
A. C. Niemeyer  and
Oreste Panaia
W. E. Longstaff
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia, e-mail: longstaf@maths.uwa.edu.au, alice@maths.uwa.edu.au, oreste@maths.uwa.edu.au
A. C. Niemeyer
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia, e-mail: longstaf@maths.uwa.edu.au, alice@maths.uwa.edu.au, oreste@maths.uwa.edu.au
Oreste Panaia
Affiliation:
School of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia, e-mail: longstaf@maths.uwa.edu.au, alice@maths.uwa.edu.au, oreste@maths.uwa.edu.au
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The length of every pair {A, B} of n×n complex matrices is at most 2n − 2, if n ≤ 5. That is, for n ≤ 5, the (possibly empty) words in A, B of length at most 2n − 2 span the unital algebra  generated by A, B. For every positive integer m there exist m×m complex matrices C, D such that the length of the pair {C, D} is 2m – 2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 3 , June 2006 , pp. 461 - 472
Copyright
Copyright © Australian Mathematical Society 2006

References

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